Taguchi or DOE?, continued
by John Cesarone, Ph.D., P.E.

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In our section on DOE, we started by looking at its origins in the world of statistics and agricultural science. Likewise, to understand Taguchi methods, its helps to realize that it came from the world of design engineering.  Taguchi methods start with the assumption that we are designing an engineering system, either a product to perform some intended function, or a production process to manufacture some product or item.  Since we are knowledgeable enough to be designing the system in the first place, we generally will have some understanding of the fundamental processes inherent in that system.  We have some idea of the theory behind an internal combustion engine, or behind a metal removal process or an injection molding process.  This is a completely different situation than the agricultural or biological systems discussed above, where we have no idea what's going on behind the scenes.  How do we use this knowledge to our advantage?

Basically, we use this knowledge to make our experiments more efficient.  We can skip all that extra effort that might have gone into investigating interactions that we know do not exist.  Without going into the details, it has been shown that this can decrease our level of effort by a factor of ten or twenty or more.  Sometimes much more.

Another distinction in Taguchi methods is the recognition that there are variables that are under our control, and variables that are not under our control.  In Taguchi terms, these are called Control Factors and Noise Factors, respectively.  An early step in a Taguchi analysis is to use our understanding of the fundamental process to try to identify all of the important Control Factors and Noise Factors.  In our heat treatment example above, Control Factors would include temperature, carbon potential, time in the furnace, part layout and orientation, etc.  Noise Factors might include the inherent variability in the furnace temperature distribution, errors in timing, outside air temperatures and humidities, etc.  We would want to ensure that all important Control Factors and Noise Factors are represented in our experiments.

In our full factorial DOE approach, our experimental plan was quite simple:  we tested all possible combinations of input values.  But what do we do in a Taguchi analysis?  We will test a very small subset of all possible combinations, but which combinations do we use?  The answer to this question is one of the most powerful parts of the Taguchi method.  Again, without going into too much detail, a variety of experimental plans have been published for various numbers of Control Factors and levels.  You don't have to design them for yourself; they are readily available in many textbooks.  Some examples include:

Taguchi Experimental Layouts
TaguchiNumberNumberNumber ofTests in an equivalent
Arrayof Factorsof Levels Tests RequiredFull Factoial

In this chart, the L4 array, for example, is an experimental layout designed for three control factors, each at two levels.  This might be two different materials for some new product, two manufacturing methods, and two design variations.  We might be interested in how these factors affect power consumption by our new product.  A full factorial DOE of all combinations of these factors would require eight tests, two to the third power.  The Taguchi L4 layout recommends a subset of four of these eight tests which allow the main effects to be determined.  Similarly, the L27 layout allows thirteen factors, each at three levels, to be tested with a mere 27 tests, rather than the somewhat prohibitive 1,594,323 tests required by a full factorial set of tests.  The "L", by the way, stands for Latin, since most of these designs are based on classical Latin Square layouts, appropriately pruned for efficiency.

Another major difference between DOE and Taguchi is the use of our Noise Factors.  In a traditional DOE, each combination of inputs is tested once.  In a Taguchi test, each combination which is tested (remember, we are only testing certain combinations) is tested several times.  Each of these replications is different, however, in that we use different levels of our Noise Factors.  For example, we might test a particular set of inputs at high temperature and high humidity, high temperature and low humidity, low temperature and high humidity, and low temperature and low humidity.  Even though we don't really control temperature and humidity in a production setting, we want to vary it in our tests to inject maximum variability into our experimental procedures.  This lets us determine not only which combinations of inputs give us maximum output, but which gives us the most repeatable output, which is often even more important.  Taguchi calls this quality robustness, or insensitivity to noise.

Mathematical analysis of results is similar in a Taguchi test to the analysis of a DOE.  We can still calculate average effect of each of our inputs (a.k.a., Control Factors), and the effects of some of our interactions.  However, we can also calculate effect on robustness of each of our inputs.  Taguchi recommended a signal to noise ratio to represent robustness, but a simple variance or standard deviation will work just as well and is more familiar to most engineers.  Likewise, we can calculate average affects on output and on robustness for each of our Noise Factors.  For details of these calculations, see any elementary textbook on Taguchi analysis.

One final difference from DOE remains.  Taguchi recommends a final confirming experiment be performed.  Remember that in our full factorial DOE, we tested all possible combinations of input values.  After our analysis, we determined which combination gave us the best output, and that led to our decision of what to use in the future.  Since we tested all combinations, the "winning combination" was necessarily one of our tests, and we had direct confirmation that it was, indeed, the best.  However, in a Taguchi analysis, we only performed a small fraction of all possible input combinations.  Our mathematical analysis lead us to select a certain combination of input decisions as "optimal", even though we might not have tested that particular combination.  Indeed, if we performed an L16 test, we only did .046% (15 out of 32,768) of the possible input combinations; chances are the recommended combination was not one of our actual tests.  So, just to make sure, it is always a good idea to do one more test, using the combination of inputs (that is, Control Factor levels) that our analysis recommended.  If it does indeed perform as predicted, we know we have a good solution.  Is it really, truly, the best possible combination?  We'll never really know, but odds are it is pretty darn good, and our confirming experiment shows us just how good it is.

You can see why this confirming test makes more sense in engineering situations than in, say, agricultural situations.  You don't want to run one final crop growing experiment, wasting another entire year.  However, you can always hold back one engineering prototype from your initial round of experiments, and run one more test using your recommended inputs, after your analysis is complete, just to make sure.